The specification WO 01/35442 shows a UV radiator having a tubular discharge vessel. Arranged centrally and axially within the discharge vessel is a coiled electrode. Provided on the outside of the discharge vessel are a number of strip-shaped electrodes extending parallel to the tube axis and distributed evenly over the circumference. As a result, the radiator essentially radiates evenly over the entire circumference, i.e. rotationally symmetrically, in a non-directional manner. In order for it to be possible for planar surfaces to be irradiated efficiently, it is necessary to use additional reflectors which deflect as much radiation as possible evenly onto the surface to be irradiated. In order also to be able to produce radiators having lengths of more than 20 cm, a holder, for example an axial supporting tube, is provided for the central inner electrode. However, in the case of very long radiators, in particular longer than approximately 1 m, production is increasingly difficult owing to the increasing risk of the supporting tube breaking. On the other hand, it is necessary to prevent the inner electrode from sagging, since this would have a negative effect on the uniformity of the production of radiation along the entire radiator.